Functions, Domain, and Range Vocabulary

A collection of vocabulary terms based on lecture notes covering the definitions of functions, relations, and the various notations used for domain and range.

Domain

The set of all inputs or first elements in a relation.

Range

The set of all outputs or second elements actually used in a relation.

Function (one-to-one)

A relation where one input corresponds to exactly one output.

Not a Function (one-to-many)

A relation where one input corresponds to many outputs.

Function (many-to-one)

A relation where many inputs correspond to one single output.

Interval Notation

A notation used to express values that form a continuous interval on the number line, such as $[-1, 5]$.

Set-builder Notation

A shorthand used to describe a set by specifying a property its members must satisfy, for example: $\{x \mid -1 \leq x \leq 5\}$.

Square Brackets ($[]$)

Symbols used in interval notation to indicate that the endpoint values are included in the set.

Repeating Values Rule

The requirement that when writing the domain and range, values should not be repeated even if they appear multiple times in the set of ordered pairs.

Input (x) and Output (y)

The domain always comes from the input or $x$-values, while the range comes from the output or $y$-values.

Real Numbers Set Notation

Expressed as $\{x \mid x \in \mathbb{R}\}$, representing the set of all $x$ such that $x$ is an element of the real numbers.